1. Field of the Invention
This invention relates to an electrical circuit for modifying or linearizing the output of an electrical signal producing device.
2. Description of the Prior Art
The need for circuits which can alter a signal in a predictable way to remove an unwanted non-linearity has been a persistent one to instrument designers. The electrical signals derived from common transducers of physical variables are often non-linear in that, for even increments of physical change, they produce varying increments of electrical signal depending on the magnitude of the variable. Thus, for example, thermocouples employing the Seebeck effect are used to transduce temperature into voltage. The input/output relationship for such thermocouples is quite non-linear in that, for example, at 100.degree. C. a thermocouple designated as type "R" produces an output change of 7.5 micro-volt per degree Centigrade change in temperature, whereas at 1000.degree. C., the output change is 13.75 micro-volt per degree Centigrade. There are many other thermocouple types designated for example as J, K, T, E, B, etc., each of which has its own temperature-to-voltage relationship and each one of which is non-linear to some measure. Still other transducers produce non-linear responses. Further examples are: flow transducers based on the differential pressure or flow head difference principle which are characterized by an output which is proportional to some power of the flow and radiation sensors, the output of which is approximately related to the fourth power of the absolute temperature being sensed. Still other examples could be cited.
The electrical signals from transducers, such as those mentioned, are used for indication, recording, and/or controlling of the physical variable of interest. The fact that the signals are a non-linear representation of the physical variable is a problem of perception to the human observer whose expectation is that the indication or recording directly corresponds to the physical variable, rather than a non-linear electrical representation, and is stated in the applicable engineering units, such as degree Fahrenheit, gal/min, degree Kelvin, etc.
The problem of producing the acceptable presentation of a signal which is non-linearly related to its source physical variable has been solved in the past in various ways. To name but a few consider: use of non-uniform scales or charts, use of corrective linkage and use of circuit components, the non-linearity of which is opposite to that for which correction is desired. Also, linearizing circuits, which depend on segmenting the non-linear electrical representation of a physical measurement and approximating each segment by a linear response have been used. The circuit of the present invention falls into this latter category.
It is well known that a non-linear transducer, when combined in series with a correcting or linearizing circuit element which has a non-linearity exactly of the opposite type, will produce a combined response which is directly, or linearly, proportional to the physical variable. Thus, if the transducer has an output which is proportional to the square of the physical quantity, then a correcting circuit which has an output proportional to the square root of its input will, when combined, produce an output which is linearly proportional to the physical quantity. For every single valued non-linear function in a transducer, there is a linearizing function which is the reciprocal of the former and which when combined with the former produces the desired linear output presentation. The non-linear functions typical of many physical quanity transducers, such as those already mentioned, are subtle and complex. Rather than being represented by mathematical functions, they are often described in tabular form.
The degree of non-linear correction which is required in a given situation of indication, recording or controlling depends upon the use to which the result is to be subjected. Thus, if the result is used to establish the obligation of the buyer of a transferred commodity to the seller then a high degree of accuracy is required. On the other hand, if the information is only used to enlighten passersby as to the current ambient temperature then lesser accuracy or correction of non-linearity will suffice. Thus, correction is a matter of degree, with achievement being related to the extent of correcting techniques applied.
A standard technique for approximating ideal corrective functions is by means of connected variously inclined linear segments also known as a piece-wise linear approximation of a function. The matter is illustrated in FIG. 1 along with the errors which result when the piece-wise linear approximation is applied to the correction of a smooth function. While some error results, segments can always be chosen and distributed to keep the results within the desired error boundary.